```ts
/**
 * Safe division of two numbers.
 * Throws an Error if the divisor is zero (including -0) or if any argument is not a finite number.
 *
 * @param {number} a - The dividend.
 * @param {number} b - The divisor.
 * @returns {number} - The result of the division.
 */
export function safeDivide(a: number, b: number): number {
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error('Both arguments must be finite numbers.');
  }
  if (b === 0 || b === -0) {
    throw new Error('Divisor cannot be zero.');
  }
  return a / b;
}
```